OK. So I have tried getting real close, touching in fact and they still just frame shift out. I guess my guns just are not powerful enough to take em down fast enough.
Our your aim!
Seriously though, if you have lasers the best way to fire at full power and in a sustained manner is to have 4 pips in WEP, otherwise your lasers overheat and you need to wait to cool them down for longer periods, and that makes you kill your target in more time... but in the other hand 4 pips in WEP prevents you from having those same pips in ENG to chase fast, so it really comes down to that balance and how well you manage those pips to be in the right place at the right time, all the while managing your speed appropriately.
Skill!
Getting closer to them makes their FSD to charge slower but it wont stop it. There will always be a fair share of NPC that will escape no matter how fast you are (maybe they activated the FSD very early on, who knows) but others wont. The better you get at a) managing your energy system pips, b) your speed and c) your aim then the more kills you ll get and the less they ll escape.
Also you need to maximize the time you shoot effectively at your target so to minimize your time to kill and the time he ll have to escape:
The better you get at maneuvering the more time you ll spend effectively shooting at your opponent, as opposed to longer "jousting" passes that minimize the time you have for shooting. Maneuvering well means trying to maximize the time you spend facing your opponent at weapon range while minimizing the time your opponent does that. "Jousting" passes (although a valid tactic especially for ships with the better weapons) are not the most effective way to achieve that. Learning how to get the most out of your ship turning rates within the "blue zone", use of boosters and assist off will help you with that.